Analysis of the Monte Carlo Image Creation by Uniform Separation

This paper considers the uniform separation technique of integration domain for Monte Carlo image creation. Uniform Separation technique is based on symmetrical separation into small equal size sub-domains to solve the rendering equation which describes the photons propagation in a virtual scene. It tries to reduce the variance at solving the rendering equation pixel by pixel in the image pixels matrix. Our goal is to analyze and study the Monte Carlo estimators by Uniform Separation for numerical treatment of the rendering equation, as well as the influence over the total process of in age creation. We develop our consideration on the base of mathematical theory for Monte Carlo estimations and the experience of image creation. New results for the symmetric separation of integration domain are obtained and presented.